In Judaism, while not obligated to, the Jews wear Tallit and Teffilin during some prayers.
What about the Gentiles - are there special clothes or items for righteous Gentiles to wear during prayers?
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Let me just outline some basic ideas:
Judaism does not deal with the details of Gentile observance beyond the 7 Noahide laws.
Prayer is not one of those laws. Gentiles are free to express themselves in prayers and praises (or bring the sacrifices to the Jewish Temple once it returns B"H) in any way they like because those are optional.
Gentiles (and Jews also) are not divided into righteous and sinful, the same laws apply to all.
Anything that does not override the 7 laws (idolatrous or adulterous pictures, for instance) would be fine.
There is no obligation for a Noahide to wear garments for prayers (if they do pray). The main point is that Noahides should not create for themself (in their own mind) a religious precept to wear a specific garment (something like a Jewish tallis or something similar to it), because he would be creating for himself an innovated commandment, which is forbidden.